Let $\mathrm{\π}\: E\to M$be a fiber bundle.Then ProjectionTransformation(n, m) defines the canonical projection map of the jet space $J^n\left(E\right)$to $J^m\left(E\right)\.$

The command ProjectionTransformation is part of the DifferentialGeometry:-JetCalculus package. It can be used in the form ProjectionTransformation(...) only after executing the commands with(DifferentialGeometry) and with(JetCalculus), but can always be used by executing DifferentialGeometry:-JetCalculus:-ProjectionTransformation(...).

$\mathrm{with}\left(\mathrm{DifferentialGeometry}\right)\:$$\mathrm{with}\left(\mathrm{JetCalculus}\right)\:$

$\mathrm{DGsetup}\left(\left[x\,y\right]\,\left[u\right]\,E\,6\right)\:$

$\mathrm{\Π1}≔\mathrm{ProjectionTransformation}\left(6\,3\right)$

$\mathrm{\Π1}:=\left[x=x\,y=y\,u_{\left[\right]}=u_{\left[\right]}\,u_1=u_1\,u_2=u_2\,u_{1,1}=u_{1,1}\,u_{1,2}=u_{1,2}\,u_{2,2}=u_{2,2}\,u_{1,1,1}=u_{1,1,1}\,u_{1,1,2}=u_{1,1,2}\,u_{1,2,2}=u_{1,2,2}\,u_{2,2,2}=u_{2,2,2}\right]$

$\mathrm{Tools}:-\mathrm{DGinfo}\left(\mathrm{\Π1}\,''DomainFrame''\right),\mathrm{Tools}:-\mathrm{DGinfo}\left(\mathrm{\Π1}\,''DomainOrder''\right)$

$E\,6$

$\mathrm{Tools}:-\mathrm{DGinfo}\left(\mathrm{\Π1}\,''RangeFrame''\right),\mathrm{Tools}:-\mathrm{DGinfo}\left(\mathrm{\Π1}\,''RangeOrder''\right)$

$E\,3$